Chap. 6: Applications of Macroscopic Balances 1. Introduction • Conservation of mass, energy, & momentum Simplified version at steady states Ex.) Expansion losses in No. of unknowns > No. of eqn. (p1-p2) or F must be known

• Simpler applications Case I: Viscous losses for a given flow P from EOM  Losses from EOE (prior information F) Case II: Force for a given flow P from EOE  Force from EOM (prior information viscous losses) Case III: Pressure change for a given flow Known F  P from EOM or Known viscous losses  P from EOE

2. Losses in Expansion • Losses in flow of an incompressible fluid through an expansion (Table 5-1) • P from EOM  Losses from EOE • Assumption: turbulent, uniform velocity over cross-section at positions 1 and 2 (==1) F component in flow direction Fluid pressure on the expansion surface at plane “e” Let’s decompose F: Tangential friction drag along the walls (Pe: gage pres., outside pres.=0)

pep1 (small distance) (pep1, short segment, Ve=V1) • From Bernoulli eq. Borda-Carnot eq.: (See Table 5-1)

3. Force on a Reducing Bend Horizontal reducing bend 3. Force on a Reducing Bend • Force necessary to maintain a 90o reducing bend • P from EOE  Force from EOM • Incompressible fluid, turbulent (flat velocity, ==1, <V>=V), no shaft work (No gravity in xy-plane)

4. Jet Ejector Uniform Vs & Vj at pt. 1 Uniform velocity at pt. 2 (p2 - p1) (positive ?)

(No gravity, F=0)

5. Flow through an Orifice • Q & p ? • p from EOM or EOE (but, from EOE here due to difficulty to measure F) • One of flow measuring systems e.g., venturi meter, rotameter, turbine meter • Incompressible, uniform velocity

6. Pitot Tube (stagnation pt.) • Velocity profiles in a flowing system by means of pressure measurement • p from Bernoulli eq. (stagnation pres.) • Useful for high Re condition (viscous terms should be considered at low Re)

Re=1.2*105 Re=800

(valid for 50 < Re < 100) 7. Diameter of a Free Jet Laminar flow Uniform velocity Negligible (valid for 50 < Re < 100)

8. Manifold Negligible Horizontal Horizontal Negligible Pressure recovery Negligible Horizontal Horizontal Negligible Side flow